NCERT Class 10 Mathematics Mathematics: Chapter 14 — MATHEMATICS
This chapter introduces the concept of probability in mathematics for Class 10 students under the CBSE curriculum. It begins by defining probability as a theoretical approach, contrasting it with experimental probability. The text explains the assumption of equally likely outcomes using examples like tossing a fair coin and throwing a fair die. It clarifies that not all experiments have equally likely outcomes, such as drawing balls of different colors from a bag. The chapter then presents the classical definition of theoretical probability: P(E) = (Number of outcomes favourable to E) / (Total number of all possible outcomes of the experiment), assuming equally likely outcomes. This theoretical approach, developed by Pierre Simon Laplace, allows for the calculation of probability without repeating experiments, which is crucial for complex or unrepeatable scenarios. This foundational understanding is essential for further study in statistics and data analysis.
Quick info
| Board | CBSE / NCERT |
|---|---|
| Class | Class 10 |
| Subject | Mathematics |
| Book | Mathematics |
| Chapter | Chapter 14 — MATHEMATICS |
| Language | English |
| PDF type | NCERT Textbook |
| Session | CBSE 2026 |
| Reading time | 4 minutes |
| Word count | 660 |
Learning outcomes
- Understand the concept of probability as a theoretical approach.
- Differentiate between equally likely and not equally likely outcomes.
- Define and apply the classical definition of theoretical probability.
- Recognize the assumptions behind theoretical probability calculations.
Vocabulary
| Word | Meaning |
|---|---|
| Probability | The measure of the likelihood that an event will occur. |
| Theoretical Approach | Calculating probability based on assumptions and logical reasoning rather than experiments. |
| Fair Coin | A coin that is symmetrical, with no bias towards landing on one side over the other. |
| Random Toss | A coin toss performed freely without bias or interference. |
| Equally Likely | Outcomes that have the same chance of occurring. |
| Unbiased | Having no prejudice or preference; in probability, meaning all outcomes are equally likely. |
| Experiment | A process or action that produces one or more outcomes. |
| Outcome | A possible result of an experiment. |
| Die | A small cube with faces numbered from 1 to 6, used in games of chance. |
| Empirical Probability | Probability calculated based on the results of an actual experiment or observation. |
| Classical Probability | Theoretical probability defined as the ratio of favorable outcomes to total possible outcomes. |
| Favourable Outcome | An outcome that satisfies the condition of the event being considered. |
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Practice questions
- What are the possible outcomes when a fair coin is tossed? Answer: Head or Tail.
- Are the outcomes of throwing a fair die equally likely? Answer: Yes, each number from 1 to 6 has an equal chance of appearing.
- Give an example where outcomes are not equally likely. Answer: Drawing a ball from a bag containing 4 red balls and 1 blue ball; drawing a red ball is more likely than drawing a blue ball.
- State the formula for theoretical probability of an event E. Answer: P(E) = (Number of outcomes favourable to E) / (Total number of all possible outcomes of the experiment).
- Who gave the definition of theoretical probability in 1795? Answer: Pierre Simon Laplace.
Frequently asked questions
What is the main difference between experimental and theoretical probability?
Experimental probability is based on the results of actual trials, while theoretical probability is calculated using logical reasoning and assumptions, like equally likely outcomes.
When can we use the theoretical definition of probability?
We can use the theoretical definition when the outcomes of the experiment are assumed to be equally likely.
What does it mean for outcomes to be 'equally likely'?
Equally likely outcomes means that each possible result of an experiment has the same chance of occurring.
Why is the assumption of 'equally likely outcomes' important?
This assumption is crucial for directly calculating the exact (theoretical) probability without needing to repeat the experiment many times.
What are the possible outcomes of tossing a fair coin?
The possible outcomes are 'Head' and 'Tail'.
What are the possible outcomes of throwing a fair die?
The possible outcomes are the numbers 1, 2, 3, 4, 5, and 6.
Can all experiments have equally likely outcomes?
No, not all experiments necessarily have equally likely outcomes. For example, drawing a colored ball from a bag with unequal numbers of balls of different colors.
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NCERT Class 10 Mathematics — Mathematics — Chapter 14 — MATHEMATICS. Verified by NCERT Help Editorial Team. Reviewed on 29 Jul 2026. Last updated 10 Aug 2026.